The Best Writing on Mathematics 2017

In the eight volume of this successful series, Pitici has collected 19 papers on mathematics published in 2016, reprinted and typeset in a uniform way. Six of the previous volumes (2011-2016) were reviewed in this EMS review database, which you can recover by searching for "Pitici" with the search tool. The general concept and the practical realisation has not been changed in this volume.

It may be useful to recall that the papers here, like in the previous anthologies, are not mathematical research papers in the usual sense, but they are papers about mathematics and mathematicians and how their work relates to society. Here again we thus find papers about history, philosophy, art and culture, education, economics, and many other aspects of society. Sometimes it are these factors that influence mathematics, sometimes it is the other way around, but it illustrates that mathematics is an integral part of society and hence deserves general interest.

Some examples of these relations: Mathematics seen as a system producing products that have economic, legal, and social effects (Ph.J.Davis), just realize how mind-blowingly large the largest known prime number is (E. Lamb), how to describe random growth in nature (K. Hartnett), Richard Guy, the man who knows everything and who was a friend of Paul Erdős turned 100 in 2016 (S. Roberts), inverse yogiisms are mathematical statements that are literally true but hide or suggest something untrue, and thus are prone to misinterpretation (L.N. Trefethen), how I acquired a bronze statue of Ramanujan (G.L. Alexaderson), who would have won the Fields Medal if it had existed 150 years ago (J. Gray), what arguments are used in the ongoing debate about the human brain being Bayesian or not (R. Bain), what is and is not possible in prediction and forecasting (G. Southorn). These are just a few of the general subjects.

Somewhat more mathematical are contributions about the creation of symmetric fractals (L. Riddle) and another one about the use of projective` geometry to explain the tilt illusion of the moon (M. Frantz). Mathematics and art are walking side by side in an analysis of the painting of Luca Pacioli (ca. 1500) where the artist wants to show his craftsmanship by painting a glass rhombicuboctahedron half filled with water in a corner of the painting. A careful analysis of the angles and the perspective of this object allows to conclude that it was almost certainly added by a different painter and even the size and the position of the object with respect to the painter can be estimated (C.H. Sequin, R Shiau). More applied art in an analysis of Islamic girih decoration, not in the plane this time but on the curved surfaces of domes (M. Kasraei et al).

In the realm of mathematics education we have a contribution where it is advised that we should let children use their fingers for counting (J. Boaler, L. Chen). Other papers dealing with the subject are discussing how to explain the logarithm with a piece of string and using the catenary curve (v. Blåsjö), why one should be careful and not apply a simple mechanical cause-effect analysis when researching educational processes (J. Mason), what are the threshold concepts in undergraduate mathematics teaching, that are the hurdles, the crucial concepts to be understood properly before one should continue with subsequent material (S. Breen, A. O'Shea).

A problematic characteristic of mathematics, at least in an educational context, is its abstraction. On a more philosophical level the method of abstraction applied in mathematics and how this is different from an axiomatic approach is also discussed in a longer paper (J.-P. Marquis). The limits of mathematics and science in general is revealed in paradoxes and contradictions (N.S. Yanofsky). The latter is basically a summary of what is more elaborated in this author's book The Outer Limits of Reason (MIT Press, 2016).

This very brief enumeration does not give proper credit to the deeper contents, but it at least illustrates the breadth of the subjects covered. The number of papers in each volume of the series is usually between 20 to 24, with a peak in the 2015 and 2016 issues of about 30 papers. This 2017 volume is back to 19 and is about half the number of pages of 2016. This does not necessarily mean that the number of papers in this particular area has reduced. Pitici introduces the topics of the issue in his editorial, but, as usual, this introduction also mentions in a paragraph `More Writings on Mathematics' a number of books (a list of 68 books) whose contents perfectly blends with the subjects that are selected in this series. Moreover at the end if this collection 14 more pages list references to papers that could also have been selected, but were not, and 6 pages listing references to interesting book reviews, to notable interviews, memorial notes, obituaries, and to special journal issues. Thus there is so much more to be explored.

What is found on all these writings on mathematics is an illustration of what Pitici describes in in his introduction as follows: "Mathematics is a domain of clarity and obscurity, of enchantment and boredom, of unperturbed neatness and of puzzling paradox, of apodictic truth and arguable interpretation. The pieces in this volume once again demonstrate the dynamic coexistence of opposite characteristics of mathematics — and show that mathematics is anything but the dull subject serviced by an increasing powerful but stultifying educational bureaucracy unable to grasp, appreciate, promote, and teach the creative and imaginative sides of mathematics".

Reviewer:

Adhemar Bultheel

Book details

Mircea Pitici has selected once more a series of papers on mathematical subjects that are not so easily found in the literature and that will enjoy mathematicians as well as non-mathematicians with interest in science. It is the eight volume in this wonderful series.